41
votes
What value is there in requiring students to answer word problems in complete sentences?
Yes, there is mathematical pedagogical value in the usage of complete sentences - but this does not only refer to "answers" and not only to "word problems", but to all parts of the ...
- 1,637
40
votes
What can (and should) an educator do about ambiguous terms like "triangle", "square", etc?
I'm confused. Are you really going to try to make this sort of distinction when teaching geometric figures to students "around 9-13 years old"? Students that age (and engineers my age -- ...
- 585
37
votes
What value is there in requiring students to answer word problems in complete sentences?
I do think there is value in expecting students to give answers in correct English. It will certainly help when they start to face longer and less structured questions.
However, the example you give ...
- 459
25
votes
What can (and should) an educator do about ambiguous terms like "triangle", "square", etc?
One encounters exactly the same issue teaching multivariable calculus when one treats integrals over three-dimensional regions and integrals over the surfaces that are their boundaries. In particular ...
- 5,719
23
votes
What value is there in requiring students to answer word problems in complete sentences?
An example of a problem where phrasing the answer as a sentence might prevent mistakes and encourage understanding is:
Alice goes to the store with \$2.00. A gumball costs \$0.80. How many gumballs ...
- 339
22
votes
What can (and should) an educator do about ambiguous terms like "triangle", "square", etc?
I think the distinction you are raising is not natural to students at this age. I teach undergraduates and graduate students, not elementary schoolers, but I find that it is not natural for ...
- 5,108
19
votes
Can we save the word "unique"?
I don't see this as a major issue, nor do I believe that the word "unique" is in any particular need of saving. There are a large number of terms in mathematics which correspond to ...
- 7,433
17
votes
Examples of Mathematical Slang
One of the most colorful names I have heard is the Chicken Mc Nugget theorem:
for any two relatively prime positive integers $m,n$, the greatest integer that cannot be written in the form $am + bn$ ...
- 500
16
votes
Can students tell the difference between the "definition if" and the "theorem if"?
Not formal research, but some decades of experience teaching both undergrad and graduate level courses, and "editing" PhD theses and such:
It appears that even many serious professional ...
- 14k
16
votes
What value is there in requiring students to declare the dimensions of an answer when it is already clear from context?
In my experience with remedial-level community-college students (USA), it is simply never the case that the units are trivially "clear from context". I can easily see some of my former ...
- 23.6k
13
votes
What is it called when terms disappear when reducing fractions?
So German "$b$ kürzt sich weg" becomes in English "$b$ cancels out". We may also say "$b$ is eliminated".
- 7,273
13
votes
How to reduce ambiguity in the following question?
The ambiguous answer is relatively correct (actually you need to know how old they are at the start of the problem). But each fission is an individual splitting, not a generation.
Perhaps this:
A ...
- 131
12
votes
Examples of Mathematical Slang
How about the shoelace formula for the area of an arbitrary
simple polygon?
(Image from Wikipedia.)
The formula computes the ...
- 29k
12
votes
Examples of Mathematical Slang
In Central Mexico, the expression
\begin{equation}
x_{\pm} = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\end{equation}
that solves quadratic equations of the form $ax^2 + bx + c = 0$ is called "fórmula del ...
- 336
12
votes
What's the common word for equations and inequalities?
My phrase has always been math "statement". Equations and inequalities clearly assert/state a relationship between two or more things.
My go-to direction using this would be something like: &...
- 8,856
12
votes
What can (and should) an educator do about ambiguous terms like "triangle", "square", etc?
Educator here who has worked with many students in the aforementioned age range (9-13) on triangles and squares. In my experience, it has never come up that a confusion between the boundary and the ...
- 520
12
votes
What value is there in requiring students to answer word problems in complete sentences?
Jochen's answer is very good. To add to it, here's the reasoning I was given as a student: answering in full sentences makes students think about the answer in different psychological context. This ...
- 221
11
votes
Is 'For all $x$' an abuse of language in math?
No, there is no abuse of language here.
$x$ and $y$ are placeholders that stand for individual numbers, and your second suggestion captures this: For each number we can insert in place of $x$ and $y$, ...
- 219
10
votes
Examples of Mathematical Slang
In Russian, the Squeeze Theorem (a.k.a. The Pinching Theorem) is called "Теорема о двух милиционерах" — "Two Policemen Theorem". The idea is that if two policemen are holding a criminal between ...
- 854
10
votes
Examples of Mathematical Slang
I often refer to the identities $(AB)^{-1} = B^{-1}A^{-1}$ or $(AB)^T = B^TA^T$ as the socks-shoes identity. I'm not sure how wide-spread this is, I certainly did not invent it and I'm pretty sure I'...
- 10.7k
10
votes
Accepted
What is it called when terms disappear when reducing fractions?
If you continue the operations until
$$\require{cancel}\frac{x}{b}=\frac{c}{b},\qquad\left(\frac{x}{b}\right)b=\left(\frac{c}{b}\right)b,\qquad x\left(\frac{b}{b}\right)=c\left(\frac{b}{b}\right),\...
- 10.7k
10
votes
What value is there in requiring students to declare the dimensions of an answer when it is already clear from context?
The legitimate purpose of this is trying to get the student to actually read the question and take note of the fact that there is indeed a context.
Many students approach mathematical exercises as &...
- 722
9
votes
Examples of Mathematical Slang
If you simplify a term by adding and subtracting something you call this a "nahrhafte Null" in German (probably translates to "nutritious null"?).
- 2,972
9
votes
What can (and should) an educator do about ambiguous terms like "triangle", "square", etc?
I confess, when you start talking about 1-D triangles, my own first thought is "how can you have non-colinear points in 1-D?". So, I imagine most students that age will have a far more ...
- 91
9
votes
What value is there in requiring students to answer word problems in complete sentences?
I do think this has (some) pedagogical value, specifically for word problems.
Word problems are designed to give students practice applying math to real-world situations. Doing this effectively means ...
- 250
8
votes
What is it called when terms disappear when reducing fractions?
In general, as others have noted, if you have an equation such as
$$\frac{x}{b}=\frac{c}b$$
The step to get from there to
$$x=c$$
is typically referred to as cancelling the denominator. More generally,...
- 777
7
votes
Examples of Mathematical Slang
My elementary students always wanted to know the name of the symbol shown here:
We called it the division house as did many of my colleagues, but my students wanted a mathematical name. We therefore ...
- 7,929
7
votes
Accepted
Phrasing the Van Hiele levels in student-friendly language
The argument has been made that this is sort of a misappropriation of the terms, because the levels are meant to define levels of understanding rather than levels of detail. I'm assuming what you're ...
- 384
7
votes
Can we save the word "unique"?
To my mind the defintion "Every x has a unique f(x)" of one-to-one is problematic because "has a unique" is neither clear English nor precise. The definition is usually stated as "$f(x) = f(y)$ ...
- 5,719
7
votes
How to word this exercise about converting "English" into interval notation?
This is my suggestion.
Write each set of numbers in interval notation.
(a) All real numbers between 5 and 7, including 5 but not including 7.
(b) All real numbers between 1 and 10, including both 1 ...
- 7,929
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